Sharp Poincaré-type inequality for the Gaussian measure on the boundary of convex sets

Alexander V. Kolesnikov; Emanuel Milman

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arXiv · 1601.02925

Sharp Poincaré-type inequality for the Gaussian measure on the boundary of convex sets

Alexander V. Kolesnikov·Emanuel Milman

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Abstract

A sharp Poincaré-type inequality is derived for the restriction of the Gaussian measure on the boundary of a convex set. In particular, it implies a Gaussian mean-curvature inequality and a Gaussian iso second-variation inequality. The new inequality is nothing but an infinitesimal form of Ehrhard's inequality for the Gaussian measure.

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Alexander V. Kolesnikov, Emanuel Milman. 2016-07-14. Sharp Poincaré-type inequality for the Gaussian measure on the boundary of convex sets. https://arxiv.org/abs/1601.02925

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